In an electrolytic cell, the cathode is where the reduction reaction takes place. To determine which substance will be reduced, we need to compare the standard reduction potentials of the ions involved.
1. Standard Reduction Potentials:
- For nickel:
\( Ni^{2+} + 2e^- \rightarrow Ni(s) \)
\( E° = -0.25 \text{ V} \)
- For copper:
\( Cu^{2+} + 2e^- \rightarrow Cu(s) \)
\( E° = +0.34 \text{ V} \)
2. Identify Which Ion is More Easily Reduced:
Reduction occurs more easily in the ion with the higher (more positive) reduction potential. In this case, copper has a higher standard reduction potential (+0.34 V) compared to nickel (-0.25 V). This means copper ions (\( Cu^{2+} \)) are reduced more readily than nickel ions (\( Ni^{2+} \)).
3. Determine the Cathode:
In the electrolytic cell, the site where the reduction of \( Cu^{2+} \) ions to solid copper (\( Cu(s) \)) occurs will be the cathode.
Since solid copper (\( Cu(s) \)) is the substance where the reduction happens, we conclude that:
The cathode in a nickel and copper electrolytic cell is \( Cu(s) \).
Hence, the correct answer is:
C. [tex]\( Cu(s) \)[/tex]
